Chronic inflammation does not mediate the effect of adiposity on grip strength: results from a multivariable Mendelian randomization study

The relationship between adiposity and grip strength (GS) is complex. We investigated whether one pathway through which adiposity affects GS was via chronic inflammation. 367,583 UK Biobank participants had body mass index (BMI), waist-hip-ratio (WHR), C-reactive protein (CRP) and GS data. Univariable Mendelian randomization (MR) and multivariable Mendelian randomization (MVMR) analyses (using inverse variance weighted (IVW) weighted median estimates (WME) and MR-Egger models) estimated total, direct and indirect effects of adiposity traits on GS using genetic instruments for BMI and WHR (exposures) and CRP (mediator). Observational findings suggested higher BMI was associated with stronger grip, e.g., in males, per standard deviation (SD) higher BMI, GS was higher by 0.48 kg (95% confidence interval(CI):0.44,0.51), independent of CRP. For males MR estimates were directionally consistent; for females, estimates were consistent with the null. Observational findings for WHR suggested that higher WHR was associated with weaker grip. In multivariable MR-IVW analyses, effects in males were consistent with the null. In females, there were consistent effects such that higher WHR was associated with stronger grip, e.g., 1-SD higher WHR was associated with 1.25 kg (MVMR-Egger; 95% CI:0.72,1.78) stronger grip, independent of CRP. Across sexes and adiposity indicators, CRP’s mediating role was minor. Greater adiposity may increase GS in early old age, but effects vary by sex and adiposity location. There was no evidence that inflammation mediated these effects.


Participant selection
At the time of our study, UK Biobank had genetic data available for 487,409 participants.We applied individual-level quality control (QC) to exclude participants with excessive / minimal heterozygosity, sex mismatch, excessive genetic relatedness (more than 10 putative third-degree relatives in the kinship table), no consent, non-European ancestry, and missing QC metrics, leaving 408,480 participants for analysis.We further excluded participants with no phenotype data (N = 40, 897), leaving 367,583 participants for subsequent analyses (Figure 1).

Variable ascertainment Covariates
Potential confounders were identified from a directed acyclic graph constructed using the online tool DAGitty (https://www.dagitty.net).Information on participants' age, sex, smoking status, alcohol intake frequency and physical activity level were collected using a self-reported questionnaire at baseline.Townsend deprivation index was assigned based on postcode as a continuous measure, where a higher index indicates more deprivation.
Smoking status was a dichotomous variable defined as not currently smoking vs. currently smoking.Alcohol intake frequency was based on the question 'how often do you drink', from which a dichotomous variable was derived representing: alcohol intake less than daily vs. alcohol intake daily/almost daily.Physical activity was based on responses to the question 'Number of days per week of vigorous physical activity lasting at least 10 minutes', from which a dichotomous variable was derived: active (at least 4 days/week vigorous physical activity lasting at least 10 minutes) vs. inactive (less than 4 days/week vigorous physical activity lasting at least 10 minutes).Comorbidities (arthritis, asthma and depression) were identified as a binary variable from baseline selfreported illness data using UK Biobank code list.

Genotyping, Imputation, and quality control
Genotyping in UK Biobank was performed using two customised genome-wide arrays, with a genome-wide imputation performed using combined reference panels from UK10K, 1000 Genomes phase 3, and Haplotype Reference Consortium (HRC), resulting in 93,095,623 autosomal variants (1).We further applied quality control to exclude variants with the following criteria: Fisher information <0.3, missing call rate ≥ 5%, or MAF outside of 0.01-1 range.

Mendelian randomization (MR) analysis methods and assumptions
MR analysis uses genetic variants as proxies for exposure of interest to estimate the causal association between the exposure and outcome of interest in an instrumental variable (IV) framework.A conventional MR makes assumptions that genetic instruments for the exposure must be: -Robustly associated with the exposure.This assumption is reasonable as the genetic variants for each of the traits used in our study achieved genome-wide significance in their respective (large-scale) GWAS.
-Associated with the outcome only through exposure.
-Independent of confounders that influence the exposure and outcome after conditioning on observed confounders (2).
While the last two assumptions cannot be completely verified, we are confident in the validity of our MR estimates because i) we assessed the robustness of our findings to horizontal pleiotropy using two methods (weighted-median regression and MR-Egger) and ii) we checked whether associations existed between our adiposity SNPs and potential (area-level deprivation, smoking status, physical activity, age at recruitment, alcohol intake and comorbidities) using linear or logistic regression as appropriate (we applied a Benjamini-Hochberg false discovery rate (BH-FDR) of 0.05 to account for multiple testing).However, we acknowledge that unobserved confounding may still be present.

Univariable MR
To estimate the total effects of each adiposity indicator on grip strength we performed univariable MR utilising a pseudo two-sample MR approach (where summary statistics for genetic associations with the exposure and the outcome, typically estimated in two independent samples, were used to calculate the MR estimate).Specifically, we used the following methods:

Inverse-variance weighted
For uncorrelated genetic variant , the causal estimate  ̂ can be calculated by averaging the ratio between variant-outcome association estimate  ̂ and variant-exposure association estimate  ̂ using the inverse-variance weighted formula for multiplicative random-effect meta-analysis model, which yields: where  ̂ (or  ̂ ) and    are the coefficient and standard error from regression of, e.g., genetic variant  on grip strength  and genetic variant  on adiposity (3).

MR-Egger regression
The MR-Egger regression performs a weighted linear regression of  ̂ on the  ̂ , using the    −2 as weights and with unconstrained intercept 11 .The causal estimate  ̂ is obtained from the model: The intercept term  ̂ denotes the estimated horizontal pleiotropic effect across genetic variants, and thus, the associated p-value for the intercept term is indicative of overall horizontal pleiotropy.The MR-Egger estimates typically have low power, but we used this method to detect horizontal pleiotropy(4).
Both the IVW and MR-Egger models make several additional assumptions, including NO Measurement Error (NOME), InSIDE (Instrument Strength Independent of Direct Effect), and VIS (Variation in Instrument Strength), as detailed elsewhere (5).

Weighted median estimator
In the weighted median estimator, first the causal estimate  ̂ of each variant  is calculated with the ratio method as  ̂ =  ̂  ̂ ⁄ .Then,  ̂ are sorted (so that  ̂1 <  ̂2 < ⋯ <  ̂) and standardised weight   is assigned to the th-ordered ratio estimate.The weights are calculated using the inverse variance of the ratio estimates as ́ =  ̂    −2 .The standardised weights are   = ́ ∑ ́  ⁄ and their sum is   = 1.
If  denotes the largest integer such that the sum of weights up to and including the th estimate (   = ∑

𝑗≤𝑘
) is <0.5, the causal estimate from weighted median method  ̂ can be calculated by interpolation between the th and ( + 1)th ratio estimates as follows: This approach should provide a consistent estimate given that at least 50% of the weights are derived from valid variants and is more robust to violation of the untestable InSIDE assumption (6,7).

Multivariable MR
MVMR requires a set of SNPs which are associated with the exposure/mediator variables but do not affect the outcome other than through these variables.As per the standard univariable MR with a single exposure, these SNPs are used to predict each of the exposure variables in the model and these predicted values are then used to estimate the effect of the exposures on the outcome in a multivariable regression analysis.
To perform an MVMR analysis, the number of included instruments must but be at least equal to the number of exposures to be instrumented in the model.As with standard univariable MR it is important that the instrumental variable assumptions are satisfied.In MVMR these assumptions become: -MVMR-IV1: the exposures/mediators must be strongly predicted by the SNPs given the other exposures/mediators included in the model; -MVMR-IV2: the SNPs must be independent of the outcome given all of the exposures/mediators included in the model; and -MVMR-IV3: the SNPs must be independent of all confounders of any of the exposures/mediators and the outcome .

MVMR-IV1:
In MVMR it is necessary for the exposures/mediators to be strongly predicted by the set of SNPs; the exposures/mediators must also be strongly predicted by the SNPs conditional on the other exposures/mediators included in the estimation.In our example in which adiposity and CRP are included as exposures/mediators, the set of SNPs used as instruments must be able to strongly predict, e.g., adiposity, once the association between the SNPs and CRP has been accounted for (8,9).If this assumption is not satisfied then there will be multicollinearity between the predicted exposures/mediators and the MVMR estimates obtained will suffer from weak-instrument bias (8,10).MVMR-IV2/MVMR-IV3: MVMR analysis requires that the SNPs do not affect the outcome other than through the set of exposures/mediators included in the model.However, SNPs that affect multiple phenotypes can be included in the estimation, as long as all of those phenotypes are included as exposures/mediators.These assumptions are therefore slightly less restrictive than for univariable MR.Pleiotropy, specifically horizontal pleiotropy in which a SNP is associated with two or more phenotypes independently, is a violation of the traditional third IV assumption if any phenotype associated with the SNP (other than the exposure of interest) is also associated with the outcome.MVMR can be used as a form of pleiotropy adjustment when SNPs have potential horizontal pleiotropic effects on a phenotype that influences the outcome as this phenotype is included as an additional exposure in the analysis, therefore accounting for the pleiotropic pathway.It is still necessary however to test for heterogeneity in the SNP-outcome association as an indicator of potential pleiotropy in MVMR that has not been accounted for and this can be achieved using an adjusted Cochran Q statistic with summary data (9).There are currently few methods for sensitivity analysis in MVMR if pleiotropy is suspected, however one method of analysis that can be used to adjust for pleiotropy is multivariable MR-Egger(11) which allows for directional pleiotropy which is uncorrelated with the size of the SNP-exposure association.

Allele alignment across GWAS and proxy SNP selection
In MVMR analyses, the effect of each SNP has to be obtained for its associated trait and for the other trait in the analysis (e.g., beta estimates for the 76 BMI SNPs have to be obtained for the effect on both BMI and CRP).
When identifying the SNPs in the GWAS of the other trait, we ensured that the beta from the same allele selected as the 'effect increasing' allele in the first GWAS (e.g., BMI) was selected from the other GWAS (e.g., CRP).If there was a mismatch between the alleles across the two GWAS, then the beta in the second GWAS was multiplied by -1 to ensure alignment.
Where SNPs selected from the exposure GWAS (e.g., BMI or WHR) were not available in the mediator GWAS (CRP), or vice versa, proxy SNPs were identified using the 'proxy search' facility on SNIPA (https://snipa.helmholtz-muenchen.de/snipa3/), with those selected having an LD R 2 >0.8.Where proxy SNPs were used, we checked which allele in the proxy SNP matched which allele in the original SNP.The allele frequency was used to check if this was the effect allele in the GWAS.If the allele frequency matches that of the effect allele in the GWAS then transformation of the beta was not required.If the effect allele frequency in the GWAS was for the other allele then we multiplied the reported beta by -1 to get the beta for us to use.For example, SNP rs2287019 from the BMI GWAS was not observed in the CRP GWAS and so we selected the proxy rs11672660.In the BMI GWAS, allele C (allele frequency=0.803)was used as the effect increasing allele whereas in the CRP GWAS, allele T (allele frequency=0.214)was reported as the effect allele for the proxy SNP.As the allele frequencies suggest that different alleles were used across the two GWAS, we multiplied the beta for the effect of rs11672660 on CRP by -1 to ensure alignment of alleles across the two GWAS.

BMI GWAS WHR GWAS BMI GWAS WHR GWAS BMI GWAS
Where necessary, beta coefficients were multiplied by -1 to ensure all betas represented an increase in the respective traits and allele harmonisation was done to ensure alignment of alleles for both the SNP-X and SNP-Y associations.GWAS betas, SEs and p-values taken from Locke et al. 2015. *

Table 2 : Summary statistics describing SNP-X associations for the BMI, WHR and CRP instruments: females
Where necessary, beta coefficients were multiplied by -1 to ensure all betas represented an increase in the respective traits and allele harmonisation was done to ensure alignment of alleles for both the SNP-X and SNP-Y associations.GWAS betas, SEs and p-values taken from Locke et al. 2015. *

table 4 . Direct, indirect and total effects of adiposity on grip strength estimated from structural equation models of observational data (n= 367,583) Difference (95% CI)* in grip strength (kg) by adiposity indicator
associations represent estimated mean difference in grip strength (kg) per 1 SD higher adiposity indicator.**Models adjusted for the Townsend index of deprivation, smoking status, physical activity, alcohol intake, age at recruitment, and comorbidities (arthritis, asthma and depression). *

table 5 . Estimates from univariable MR for total effect of adiposity* on grip strength (n= 367,583) Difference (95% CI) in grip strength (kg) by adiposity indicator
IVW: Inverse-variance-weighted; WME: weighted median estimator; MR-Egger: Mendelian randomisation Egger regression; *associations represent estimated mean difference in grip strength (kg) per 1 SD higher genetically predicted adiposity indicator; p-pleiotropy: p-value for overall horizontal pleiotropic effect indicated by the intercept from MR-Egger regression Supplementary

table 7 . Estimates from univariable MR for total effect of adiposity* on grip strength (kg) after removing adiposity SNPs associated with potential confounders (n= 367,583) Difference (95% CI) in grip strength (kg) by adiposity indicator
IVW: Inverse-variance-weighted; WME: weighted median estimator; MR-Egger: Mendelian randomisation Egger regression; *associations represent estimated mean difference in grip strength (kg) per 1 SD higher genetically predicted adiposity indicator; p-pleiotropy: p-value for overall horizontal pleiotropic effect indicated by the intercept from MR-Egger regression